In one image I noticed that the exhaust plumes are expanding differently - the SRB exhaust is expanding nicely, but the exhaust from the main engines appears to contract after it exits. Does this mean that the pressure in the exhaust is actually sub-atmospheric (if I put a rugged pressure meter in there, moving at the same speed as the exhaust would it read below 15 psi?) , or is it moving so fast with respect to the atmosphere that the "Bernoulli effect" causes a pressure drop across the interface, causing it to contract?

I'm looking for more than the simple answer about compromises in expansion ratio - I'd like to know if the pressure in the first stage exhaust is really sub-atmospheric in a frame moving with the exhaust itself.

$\begingroup$Not an answer, just some additional information: The booster burn time is 90 seconds, the center core 240s - That means, the booster shuts down around 20 km and never operates below 50 mbar ambient pressure. Seems reasonable to have its nozzle at a lower expansion ratio.$\endgroup$
– asdfexSep 12 '16 at 8:16

1 Answer
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Yes, the pressure of the first stage exhaust is always at least slightly subatmospheric, because that gives the maximum average ISP over the whole burn time. Rockets with boosters attached (parallel staging) often operate at the lowest possible exhaust pressure that prevents the flow from detaching from the nozzle walls. Historically, the Summerfield criterium was used, where the minimum pressure in a nozzle must be greater than 0.35...0.4*atmospheric pressure, but more recent designs use even lower pressures. For example, if I remember correctly, the Vulcain 2 was designed using the Schmucker criterium, which factors in the Mach number as well.

$\begingroup$I keep seeing discussions about optimal expansion, but this the first time I really have come face-to-face with the fact that the thrust can have such a huge force (vector) and temperature yet have such low pressure. Since it is so hot, the density must be only a few percent of atmospheric density. Amazing!$\endgroup$
– uhohSep 12 '16 at 10:24

$\begingroup$Yep - I'm just ballparking ~0.5X the pressure and ~15X temperature = "few percent". It's way out of equilibrium and some fraction of the carbon is already forming particulates, so it's a mess, but it must be greater than 1% and less than 10%.$\endgroup$
– uhohSep 13 '16 at 10:53